Scheme Programming Language :: how to derive closed form fibonacci using scheme?


	how to derive closed form fibonacci using scheme? hi How to derive closed form fibonacci using scheme (programmically, without human guidance)? Maple can do it. How can I code something like that in scheme. math.id@gmail.com skrev: > How to derive closed form fibonacci using scheme (programmically, > without human guidance)? > Maple can do it. How can I code something like that in scheme. How did you do it in Maple? -- Jens Axel Sgaard On Mar 22, 11:50 pm, Jens Axel Sgaard <use@soegaard.net> wrote: > math.id@gmail.com skrev: > > How to derive closed form fibonacci using scheme (programmically, > > without human guidance)? > > Maple can do it. How can I code something like that in scheme. > How did you do it in Maple? rsolve({F(n) = F(n-1) + F(n-2), F(1..2)=1}, F, 'genfunc'(x)); - Hide quoted text - > -- > Jens Axel Sgaard math.id@gmail.com skrev: > On Mar 22, 11:50 pm, Jens Axel Sgaard <use@soegaard.net> wrote: >> math.id@gmail.com skrev: >>> How to derive closed form fibonacci using scheme (programmically, >>> without human guidance)? >>> Maple can do it. How can I code something like that in scheme. >> How did you do it in Maple? > rsolve({F(n) = F(n-1) + F(n-2), F(1..2)=1}, F, 'genfunc'(x)); And how would you code rsolve in Maple? -- Jens Axel Sgaard On Mar 23, 5:23 am, Jens Axel Sgaard <use@soegaard.net> wrote: > math.id@gmail.com skrev: > > On Mar 22, 11:50 pm, Jens Axel Sgaard <use@soegaard.net> wrote: > >> math.id@gmail.com skrev: > >>> How to derive closed form fibonacci using scheme (programmically, > >>> without human guidance)? > >>> Maple can do it. How can I code something like that in scheme. > >> How did you do it in Maple? > > rsolve({F(n) = F(n-1) + F(n-2), F(1..2)=1}, F, 'genfunc'(x)); > And how would you code rsolve in Maple? Is that a rhetoric question? I know exactly the trick to solve it, but that was after human has already found out the trick. I'm interested in how machine can do it by itself. - Hide quoted text - > -- > Jens Axel Sgaard math.id@gmail.com skrev: > On Mar 23, 5:23 am, Jens Axel Sgaard <use@soegaard.net> wrote: >> math.id@gmail.com skrev: >>> On Mar 22, 11:50 pm, Jens Axel Sgaard <use@soegaard.net> wrote: >>>> math.id@gmail.com skrev: >>>>> How to derive closed form fibonacci using scheme (programmically, >>>>> without human guidance)? >>>>> Maple can do it. How can I code something like that in scheme. >>>> How did you do it in Maple? >>> rsolve({F(n) = F(n-1) + F(n-2), F(1..2)=1}, F, 'genfunc'(x)); >> And how would you code rsolve in Maple? > Is that a rhetoric question? It was not rhetoric. Whatever method was used in Maple can be copied in Scheme. > I know exactly the trick to solve it, but > that was after human has already found out the trick. I'm interested > in how machine can do it by itself. So the question is not as much as "How do I solve the recursive relation in Scheme (as compared to Maple", but rather ""How do I solve the a general relation (in Math)?" ? -- Jens Axel Sgaard Jens Axel Sgaard skrev: > So the question is not as much as "How do I solve the recursive relation > in Scheme (as compared to Maple", but rather ""How do I solve the a > general relation (in Math)?" ? See this PowerPoint presentation for an introduction to the general theory. It uses Fibonacci as an example. <http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fwww.cs.um...> -- Jens Axel Sgaard On Mar 22, 7:46 pm, math.id@gmail.com wrote: - Hide quoted text - > On Mar 23, 5:23 am, Jens Axel Sgaard <use@soegaard.net> wrote: > > math.id@gmail.com skrev: > > > On Mar 22, 11:50 pm, Jens Axel Sgaard <use@soegaard.net> wrote: > > >> math.id@gmail.com skrev: > > >>> How to derive closed form fibonacci using scheme (programmically, > > >>> without human guidance)? > > >>> Maple can do it. How can I code something like that in scheme. > > >> How did you do it in Maple? > > > rsolve({F(n) = F(n-1) + F(n-2), F(1..2)=1}, F, 'genfunc'(x)); > > And how would you code rsolve in Maple? > Is that a rhetoric question? I know exactly the trick to solve it, but > that was after human has already found out the trick. I'm interested > in how machine can do it by itself. http://www.cis.upenn.edu/~wilf/AeqB.html - Hide quoted text - > > -- > > Jens Axel Sgaard